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Logistic growth model: dP/dt = rP(1 - P/K). The carrying capacity is:

Answer: K.

  • A r
  • B K
  • C P₀
  • D rK

Correct answer: B. K

Explanation: Logistic equation: K is the carrying capacity (maximum sustainable population). r is growth rate.

Family of Solution Curves: y = Ax²Each value of the constant A gives ONE particular curve from the family

The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.

Concept context

Equations involving derivatives and their solutions

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